Deep Cluster Atlas (DCA)

• Deep Cluster Atlas (DCA) is a graph-guided deep embedding clustering framework that produces individualized, voxel-wise brain parcellations with high functional coherence and spatial contiguity.
• It integrates a pretrained 4D Swin-UNETR encoder with iterative spectral clustering, aligning soft centroid assignments to graph-induced spatial labels.
• The framework supports flexible resolution and anatomical scopes, significantly improving homogeneity and silhouette metrics over traditional brain atlases.

Deep Cluster Atlas (DCA) is a graph-guided deep embedding clustering framework for generating individualized, voxel-wise brain parcellations from fMRI. It is designed to maximize functional coherence while enforcing spatial contiguity, and it combines a pretrained autoencoder with spatially regularized deep clustering. In the reported formulation, DCA integrates a pretrained 4D Swin-UNETR encoder for voxel-level representations with an iterative clustering stage that aligns soft centroid assignments to spatially contiguous graph-induced labels. The framework supports flexible control over resolution and anatomical scope, generalizes to arbitrary brain structures, and is accompanied by a standardized benchmarking platform for atlas evaluation using multiple large-scale fMRI datasets (Wang et al., 1 Sep 2025).

1. Motivation and problem formulation

DCA is motivated by limitations of most existing brain atlases, which are described as predefined, group-level templates with limited flexibility and resolution. The reported examples include Yeo, Schaefer, AAL, and MMP. These atlases often fix granularity, emphasize cortical surfaces, and may neglect subcortical or white matter structures. The paper further states that group averaging obscures substantial inter-individual variability, while classical clustering on coarse features yields noisy boundaries at fine scales and ignores spatial continuity, leading to fragmented parcels or anatomically implausible regions (Wang et al., 1 Sep 2025).

Within this problem setting, DCA is defined around three explicit goals. The first is functional coherence, meaning that voxels within a parcel should have similar fMRI time courses, expressed as high within-parcel correlation. The second is spatial contiguity, meaning that parcels should form contiguous regions in voxel space. The third is flexibility in resolution and anatomical scope. Resolution is user-selectable through the number of parcels $K$, enabling multi-scale settings such as $41$, $100$, $200$, $360$, $400$, $500$, and $800$. Scope is determined by arbitrary ROI masks, allowing the method to operate on cortex, subcortex, white matter, or any other structure, and to support both individualized and group atlases (Wang et al., 1 Sep 2025).

This formulation places DCA at the intersection of individualized atlas construction, voxel-wise representation learning, and spatially constrained clustering. A plausible implication is that the method is intended not merely to improve atlas quality in an abstract sense, but to make parcellation a tunable modeling component for downstream neuroimaging analysis.

2. Representation learning and preprocessing pipeline

The representation backbone is Swin-UNETR, described as a UNET-style encoder-decoder built on Swin Transformer and pretrained with masked spatiotemporal reconstruction on 4D fMRI blocks. The reported input block size is $96 \times 96 \times 96 \times 300$, and the masking strategy zeros $80\%$ of contiguous spatiotemporal patches. The spatiotemporal masking ratio is therefore set to $41$0. The paper attributes suitability to the hierarchical shifted-window attention mechanism, which preserves local continuity and global context for voxel-wise representation learning (Wang et al., 1 Sep 2025).

The reported pretraining details are specific. Optimization uses Adam with learning rate $41$1, on $41$2 NVIDIA A100 GPUs, with batch size $41$3 for $41$4 epochs. The internal representation is temporally downsampled to $41$5, and the encoder output used for clustering is a feature map of shape $41$6, giving embedding dimensionality $41$7. After pretraining, the encoder produces voxel-level embeddings $41$8 for all voxels $41$9 in the ROI mask. During atlas construction and fine-tuning, only the final projection block of the encoder is trainable, while the remainder is fixed (Wang et al., 1 Sep 2025).

The data preprocessing pipeline is also specified. Atlas construction uses resting-state fMRI from $100$0 HCP subjects with minimal preprocessing: gradient distortion correction, motion correction, EPI distortion correction, registration to T1, and normalization to MNI152. Data are resampled to $100$1 mm isotropic resolution, and AFNI’s 3dBlurToFWHM is applied to achieve $100$2 mm FWHM. For downstream tasks on HCP, ABIDE, and ADNI, time series are masked to brain regions, detrended, and z-scored; functional connectivity is computed via Pearson correlation, and upper triangular entries are vectorized. If the feature dimensionality exceeds $100$3, PCA reduces it to $100$4 components to balance sample size and complexity (Wang et al., 1 Sep 2025).

3. Clustering objective and graph-guided optimization

DCA employs a deep embedding clustering loop that aligns soft centroid assignments to spatially contiguous graph labels derived from the embeddings. The paper explicitly contrasts this with DEC and IDEC: rather than using a Student’s $100$5 distribution for soft assignments and an auxiliary target distribution, DCA uses min-max normalized Euclidean distances and imposes spatial continuity through graph spectral clustering. It also states that there is no explicit Student’s $100$6 kernel and no separate reconstruction loss in the clustering stage (Wang et al., 1 Sep 2025).

The learnable centroids are initialized as a trainable matrix with orthogonal, L2-normalized rows such that $100$7. For each voxel embedding $100$8 and centroid $100$9, the soft assignment is defined by

$200$0

where $200$1 denotes min-max normalization and $200$2. Equivalently,

$200$3

The initialization is reported to speed early convergence, although other schemes are said to converge similarly in the end (Wang et al., 1 Sep 2025).

Spatial guidance is introduced through a voxel adjacency graph. DCA constructs a $200$4-neighborhood graph $200$5 over ROI voxels, corresponding to the $200$6 cube excluding the center and therefore capturing face, edge, and diagonal neighbors. Edge weights use cosine similarity of demeaned embeddings: $200$7 where $200$8 is the mean of $200$9. This yields a sparse adjacency matrix $360$0 with approximately $360$1 nonzeros. Spectral clustering is then performed by forming the unnormalized Laplacian $360$2, extracting the $360$3 smallest eigenvectors of $360$4, and applying K-Means to the resulting $360$5 spectral embedding to obtain hard auxiliary labels $360$6 (Wang et al., 1 Sep 2025).

Because cluster identities can permute between iterations, DCA applies the Hungarian algorithm for label alignment. The reported matching objective is

$360$7

$360$8

The new clusters are then relabeled as $360$9. This alignment step preserves cluster identity across iterative refinement (Wang et al., 1 Sep 2025).

The clustering loss is the Kullback–Leibler divergence between the aligned one-hot auxiliary labels $400$0 and the soft assignment matrix $400$1: $400$2 Gradients update the centroids and only the encoder’s final projection block; other encoder weights remain fixed. The procedure iteratively refines embeddings, reweights graph edges, recomputes spectral clusters, and updates centroids until convergence (Wang et al., 1 Sep 2025).

The paper also reports optional and ablated objectives that are not part of the main DCA objective. These include an orthogonality regularizer on the centroid matrix and a masked reconstruction loss on non-background voxels: $400$3 and

$400$4

The reported ablation indicates no significant benefit beyond the core KL loss, so the total clustering loss in the main method is just $400$5 (Wang et al., 1 Sep 2025).

4. Spatial regularization, resolution control, and anatomical scope

A defining design choice is that DCA enforces spatial contiguity via graph-based auxiliary targets rather than through an explicit Laplacian smoothness penalty in the optimization objective. The Laplacian $400$6 is used to compute spectral embeddings for contiguous clusters, and label alignment then anchors centroid assignments to these spatially coherent targets. The paper states that this avoids tuning a spatial regularization coefficient and yields single-component parcels in practice, with ablations comparing against K-Means and graph cuts (Wang et al., 1 Sep 2025).

An alternative graph cut method, weighted BFS-connected clustering, was also evaluated. The reported outcome is that spectral clustering consistently produced high homogeneity and silhouette while ensuring contiguity. This suggests that, within the evaluated design space, contiguity is treated not as a post hoc clean-up operation but as an intrinsic supervisory signal for centroid refinement (Wang et al., 1 Sep 2025).

Control over atlas resolution is explicit and user-defined. DCA supports multi-scale atlases with $400$7. It also supports arbitrary ROI masks as the anatomical domain, including examples based on FreeSurfer aparc+aseg gray matter for cortex and custom masks for subcortical or white matter parcellation. Demonstrations reported in the paper include subcortical atlases with $400$8 and white matter atlases with $400$9 (Wang et al., 1 Sep 2025).

The optimization workflow is summarized in five steps: extract voxel embeddings from the pretrained encoder; build a $500$0-NN graph with cosine weights on demeaned embeddings; run spectral clustering and align labels by the Hungarian algorithm; convert distances to soft assignments and minimize $500$1; then update centroids and the encoder’s final projection and repeat until convergence. Adam with learning rate $500$2 is used both for pretraining and fine-tuning, batch size is $500$3, and the reported hardware remains $500$4 A100 GPUs. The paper notes that voxel-wise learning is memory-intensive and that $500$5-NN is stable and competitive, while $500$6-NN degrades silhouette (Wang et al., 1 Sep 2025).

5. Benchmarking platform, metrics, and empirical results

The paper introduces a standardized benchmarking platform called AtlaScore. The reported datasets include HCP for pretraining and evaluation, with a random set of $500$7 subjects used for evaluation; HCP, ABIDE I, and ADNI for downstream tasks; and CHCP for cross-dataset generalization, where the encoder is applied without fine-tuning (Wang et al., 1 Sep 2025).

Three internal similarity metrics are reported. Global homogeneity is defined as parcel-wise mean within-parcel correlation $500$8, weighted by parcel size: $500$9 The silhouette coefficient uses dissimilarity $800$0: $800$1 DCBC is evaluated in the Appendix on a surface-based fsLR 32k representation for the left hemisphere only: $800$2 These definitions situate DCA evaluation in terms of within-parcel similarity, cluster separation, and boundary correspondence (Wang et al., 1 Sep 2025).

Across resolutions and datasets, DCA is reported to improve functional homogeneity by $800$3 and silhouette coefficient by $800$4 over state-of-the-art atlases. At $800$5 parcels on HCP, the reported comparison states that DCA improves Homogeneity by $800$6 and Silhouette by $800$7 over Schaefer. For CHCP generalization, the method is said to produce spatially contiguous parcellations with superior homogeneity and silhouette to baselines without fine-tuning (Wang et al., 1 Sep 2025).

The downstream task protocol uses linear SVC on ROI-level functional connectivity features, with upper triangular vectorization, PCA to $800$8 dimensions when needed, and $800$9-fold cross-validation across subjects. Six representative tasks are reported: gender prediction on HCP resting FC, fluid intelligence on HCP resting FC, cognitive decoding with $96 \times 96 \times 96 \times 300$0 tasks on HCP task FC, cognitive decoding with $96 \times 96 \times 96 \times 300$1 conditions on HCP task FC, ASD diagnosis on ABIDE resting FC, and AD/MCI/CN diagnosis on ADNI resting FC. Representative outcomes for DCA200 are reported as follows: gender $96 \times 96 \times 96 \times 300$2; fluid intelligence $96 \times 96 \times 96 \times 300$3; $96 \times 96 \times 96 \times 300$4-way tasks $96 \times 96 \times 96 \times 300$5; $96 \times 96 \times 96 \times 300$6-way tasks $96 \times 96 \times 96 \times 300$7; ASD $96 \times 96 \times 96 \times 300$8; AD $96 \times 96 \times 96 \times 300$9. The paper also states that cognitive decoding peaks at intermediate resolutions such as $80\%$0–$80\%$1, fingerprinting improves with finer granularity, and FC stability tends to decrease at ultra-fine scales due to reduced SNR per parcel (Wang et al., 1 Sep 2025).

A task-adapted variant is also described. By replacing the reconstruction-pretrained encoder with one fine-tuned for gender classification, the authors derive $80\%$2. Using a CNN on ROI time series, reported accuracy is $80\%$3 for individual $80\%$4, compared with $80\%$5 for Watershed100, $80\%$6 for Schaefer100, and $80\%$7 for DCA100. Using a k-GNN on sparsified FC graphs, reported accuracy is $80\%$8 for individual $80\%$9, compared with $41$00 for Schaefer100 and $41$01 for DCA100 group (Wang et al., 1 Sep 2025).

6. Group-level atlas construction, comparisons, and ablations

Although DCA is primarily individualized, the paper also specifies a procedure for constructing contiguous group atlases from individualized parcellations. Step 1 is template label selection on reliable voxels $41$02, defined as voxels absent in at most $41$03 subjects with $41$04. The method selects the top $41$05 label vectors with pairwise Hamming distance at most $41$06, where $41$07. Step 2 assigns voxels in $41$08, defined as absent in at most $41$09 subjects with $41$10, according to

$41$11

Step 3 enforces spatial contiguity by keeping the largest $41$12-connected component per parcel and reassigning unlabeled voxels to the nearest labeled neighbor, defined by smallest Hamming distance in label vectors, until the atlas is fully labeled. The reported hyperparameter choice $41$13 yields comparable coverage to MMP and the best overall generalization in ablations (Wang et al., 1 Sep 2025).

Comparisons to existing atlases are framed both against traditional group templates and individualized methods. The paper states that, versus Yeo, Schaefer, AAL, MMP, GIANT, Watershed, and Allen HR, DCA consistently yields higher homogeneity and silhouette across resolutions, particularly in fine-scale settings, while maintaining single-component parcels due to graph guidance. Versus individualized methods relying on predefined templates, DCA is described as discovering subject-specific subdivisions from data rather than replicating anatomical labels (Wang et al., 1 Sep 2025).

The ablation results clarify which components are materially responsible for performance. K-Means on raw fMRI or on embeddings yields poor homogeneity and silhouette and produces fragmented parcels. Graph cuts on raw or encoded signals improve contiguity but still produce isolated regions and lower metrics than the KL-aligned iterative refinement of DCA. At $41$14, DCA is reported to achieve homogeneity $41$15, silhouette $41$16, and approximately $41$17 connected component per parcel; the table is described as showing a dramatic reduction in connected components relative to K-Means. Distribution-matching losses based on KL, Jensen–Shannon, and Wasserstein are reported to perform similarly, making default KL sufficient. The neighborhood-size ablation finds $41$18-NN robust, while $41$19-NN degrades silhouette, and smoothing between $41$20 and $41$21 mm produces consistent trends (Wang et al., 1 Sep 2025).

A common misconception in atlas construction is that spatial coherence necessarily requires an explicit spatial penalty in the optimization objective. The DCA formulation directly challenges that assumption: in the reported implementation, no explicit spatial loss term is used during clustering, and spatial regularization is instead mediated through graph spectral auxiliary labels aligned with centroid assignments. Another misconception is that individualized atlases must be derived from predefined anatomical templates. DCA is explicitly presented as a data-driven alternative that can be applied to arbitrary ROI masks (Wang et al., 1 Sep 2025).

7. Practical use, limitations, and prospective extensions

The practical guidance given for applying DCA is specific. Standard minimal preprocessing is recommended, including motion and EPI correction, registration, and MNI normalization. Data are resampled to $41$22 mm, and optional smoothing around $41$23 mm FWHM is reported as robust within the $41$24–$41$25 mm range. For cortex-focused tasks, the suggested starting ROI is FreeSurfer aparc+aseg gray matter, while custom masks can be defined for subcortex or white matter (Wang et al., 1 Sep 2025).

Parameter selection is task-dependent. The number of parcels $41$26 should be chosen according to the downstream objective: intermediate resolutions such as $41$27–$41$28 are reported as often optimal for cognitive decoding, finer resolutions improve fingerprinting, and clinical tasks may be resolution-insensitive. The recommended graph neighborhood is $41$29-NN with cosine weights on demeaned embeddings, the loss is $41$30 as defined above, and orthogonal-plus-normalized centroid initialization is preferred for faster early convergence. Pretraining is performed with masked spatiotemporal reconstruction using $41$31 masking on large resting-state datasets such as HCP; individualized atlas generation then freezes the encoder except for the final projection and iterates graph-guided KL alignment until convergence (Wang et al., 1 Sep 2025).

The expected outcome is a set of spatially contiguous, functionally coherent parcels at voxel resolution, with superior internal metrics and downstream utility relative to established atlases. The implementation dependencies named in the paper include AFNI (3dBlurToFWHM), DPABI, FreeSurfer, Swin-UNETR through MONAI/Transformers, and a standard Python ML stack. The code and model status is stated succinctly: “Codes and models will be released soon” (Wang et al., 1 Sep 2025).

The reported limitations are also explicit. DCA’s voxel-level training is computationally heavy, and the voxel-wise 4D modeling and graph operations impose a substantial memory footprint; ROI-restricted parcellations or sparse embedding schemes are suggested as possible strategies to improve scalability. The fixed spatial graph may underweight long-range functional relationships relative to atlases that explicitly model global connectivity. The current formulation is single-modality and uses fMRI only; future work is suggested to integrate structural, diffusion, or sEEG data, although that would require reconciling cross-modal signals in deep clustering. Sensitivity to data quality and motion remains an issue, as with any fMRI-based atlas, and no universal optimal $41$32 is claimed, with the paper distinguishing resolution-optimal, resolution-insensitive, and size-driven patterns across tasks (Wang et al., 1 Sep 2025).

Taken together, these elements define DCA as a method that couples masked-reconstruction representation learning with graph-guided deep clustering to produce individualized, voxel-wise atlases. Its central mechanism is the alignment of centroid-based soft assignments to spatially contiguous graph spectral labels through KL divergence, refining both embeddings and centroids without an explicit spatial regularizer. This suggests a broader interpretation of atlas construction as an iterative representation-and-partition co-optimization problem rather than a fixed postprocessing step on neuroimaging features.